This invention relates to sidewall coring tools. In determining the physical properties of subterranean formations, it is of great assistance to have what is commonly called cores. A core is typically a cylindrical piece of rock which has been cut from the underground formation and can vary in size and length. One type of core cutter is a type that can be used to cut the cores from the sidewall of a borehole after the borehole has already been drilled. Such a sidewall coring tool is described in U.S. Pat. No. 4,354,558 entitled, "Apparatus and Method for Drilling into the Sidewall of a Drill Hole," issued Oct. 19, 1982, with Alfred H. Jageler, Robert A. Broding and Lauren G. Kilmer as inventors. In that invention, a core barrel having a core cutting bit on the end thereof is pushed against the formation at the same time that the core barrel is rotated so that a core is cut and enters the core barrel. The present invention relates to system for retaining the core in the core barrel once the core is cut.